A multi-regional epidemic model for controlling the spread of Ebola: awareness, treatment, and travel-blocking optimal control approaches

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• 作者：Omar Zakary ; Mostafa Rachik and Ilias Elmouki
• 刊名：Mathematical Methods in the Applied Sciences
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：40
• 期：4
• 页码：1265-1279
• 全文大小：1956K
• ISSN：1099-1476

文摘

Ebola virus disease (EVD) can rapidly cause death to animals and people, for less than 1month. In addition, EVD can emerge in one region and spread to its neighbors in unprecedented durations. Such cases were reported in Guinea, Sierra Leone, and Liberia. Thus, by blocking free travelers, traders, and transporters, EVD has had also impacts on economies of those countries. In order to find effective strategies that aim to increase public knowledge about EVD and access to possible treatment while restricting movements of people coming from regions at high risk of infection, we analyze three different optimal control approaches associated with awareness campaigns, treatment, and travel-blocking operations that health policy-makers could follow in the war on EVD. Our study is based on the application of Pontryagin's maximum principle, in a multi-regional epidemic model we devise here for controlling the spread of EVD. The model is in the form of multi-differential systems that describe dynamics of susceptible, infected, and removed populations belonging to p different geographical domains with three control functions incorporated. The forward–backward sweep method with integrated progressive-regressive Runge–Kutta fourth-order schemes is followed for resolving the multi-points boundary value problems obtained. Copyright